The Annals of Probability

A variational approach to dissipative SPDEs with singular drift

Carlo Marinelli and Luca Scarpa

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We prove global well-posedness for a class of dissipative semilinear stochastic evolution equations with singular drift and multiplicative Wiener noise. In particular, the nonlinear term in the drift is the superposition operator associated to a maximal monotone graph everywhere defined on the real line, on which neither continuity nor growth assumptions are imposed. The hypotheses on the diffusion coefficient are also very general, in the sense that the noise does not need to take values in spaces of continuous, or bounded, functions in space and time. Our approach combines variational techniques with a priori estimates, both pathwise and in expectation, on solutions to regularized equations.

Article information

Ann. Probab., Volume 46, Number 3 (2018), 1455-1497.

Received: April 2016
Revised: March 2017
First available in Project Euclid: 12 April 2018

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Zentralblatt MATH identifier

Primary: 60H15: Stochastic partial differential equations [See also 35R60] 47H06: Accretive operators, dissipative operators, etc. 46N30: Applications in probability theory and statistics

Stochastic evolution equations singular drift variational approach well-posedness multiplicative noise monotone operators


Marinelli, Carlo; Scarpa, Luca. A variational approach to dissipative SPDEs with singular drift. Ann. Probab. 46 (2018), no. 3, 1455--1497. doi:10.1214/17-AOP1207.

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